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Database search
and pairwise alignments
“It is a capital mistake to theorize before one has data. Insensibly one
begins to twist facts to suit theories, instead of theories to suit facts.”
(A. Conan Doyle, A scandal in Bohemia, Strand Magazine, July 1891)
1
Table of contents
Dot plots
Simple alignments
Gap
Score matrices
Dynamic programming: The NeedlemanWunsch algorithm
Global and local alignments
Database search
Multiple sequence alignments
2
Introduction  1
Each alignment among two or more nucleotide or
amino acid sequences is an explicit assumption
about their common evolutionary history
Comparisons among related sequences have
facilitated many advances in understanding their
information content and their function
Techniques for sequence alignment and sequence
comparison, and similarity search algorithms in
biological databases are fundamental in Bioinformatics
3
Introduction  2
Sequences closely related to each other are
usually easy to align and, conversely, the quality
of an alignment is an important indicator of their
level of correlation
Sequence alignments are used to:
determine the function of a newly discovered
genetic
sequence
(comparison
with
similar
sequences)
determine the evolutionary relationships between
genes, proteins, and entire species
predict the structure and the function of new
proteins based on known “similar” proteins
4
Dot plots  1
Probably, the simplest method to reveal analogies
between two sequences consists in displaying the
similarity regions using dot plots
The dot plot is a graphical method to display
similarity
Less intuitive is its close relationship with the
alignments
The dot plot is represented by a table or a matrix
or, alternatively, in a Cartesian plane
The rows or the xaxis correspond to the residues
of a sequence, and the columns or the yaxis to the
residues of the other
5
Dot plots  2
(a)
(b)
Dot plots: (a) matrix representation and (b) graphical representation in the Cartesian plane
6
Dot plots  3
The similarity regions will thus be viewed as diagonal
lines, that proceed from SouthWest to NorthEast;
repeated sequences will produce parallel diagonals
Therefore, dot plots capture, in a single image, not
only the overall similarity between two sequences, but
also the complete set and the relative quality of the
different possible alignments
Often, some similarity may be shifted, so as to appear
on parallel, but not collinear, diagonals
This
indicates
the
presence
of
insertion/deletion phenomena occurred
in the segments between the similarity
regions
7
Dot plots  4
In the dot plot matrices, random identities
produce a high background noise (especially for
long sequences)
This happens almost always in the alignments
between nucleic acids, due to the alphabet
composed by only four letters
To reduce the noise, short
sequences (in sliding windows)
should be compared instead of
single nucleotides
In this case, the dot is reported
only when s residues coincide
within a window of dimension w
8
Dot plots  5
Increasing s values corresponds to increase the
requested precision (maximum for s = w)
Obviously, the variation of w and s has a
significant influence on the background noise
The best experimental values for w and s, with
respect to nucleotide and protein sequences, are
empirically determined by a trialanderror
process
9
Dot plots  6
A dot plot matrix, that actually considers only
identities, does not provide a true indication of
the similarity relations between proteins, since
the nonidentity among amino acids can have
very different biological implications
In fact:
In some cases the replacement of a residue with a
different one, but with very similar properties (e.g.:
leucine and isoleucine), can be almost irrelevant
In other cases, two nonidentical residues can have very
different properties
10
Simple alignments  1
A simple alignment between two sequences
consists in matching pairs of characters belonging
to the two sequences
The alignment of nucleotide or amino acid
sequences reflects their evolutionary relationship,
namely their homology, i.e. the presence of a
common ancestor
A score for homology does not exist: at any given
position of an alignment, the two sequences may
share an ancestor character or not
The overall similarity can instead be quantified by
means of a rational value
11
Simple alignments  2
In particular, in any given position within a sequence,
three types of changes may occur:
A mutation that replaces one character with another
An insertion, which adds one or more characters
A deletion, which eliminates one or more characters
In Nature, insertions and deletions are significantly
less frequent than mutations
Since there are no homologues of nucleotides inserted
or deleted, gaps are commonly added in the
alignments, in order to reflect the occurrence of this
type of changes
12
Simple alignments  3
In the simplest case, in which gaps are not allowed, the
alignment of two sequences is reduced to the choice of the
starting point for the shorter sequence
AATCTATA
AAGATA
AATCTATA
AAGATA
AATCTATA
AAGATA
To determine which of the three alignments is “optimal”, it
is necessary to establish a score to comparatively evaluate
each alignment
{
n
i1
Correspondence score, if seq1iseq2i
Noncorrespondence score, if seq1iseq2i
where n is the length of the longest sequence
For a score of nomatching/matching equal to 0/1, the three
alignments are evaluated respectively 4, 1 and 3
13
Gaps
Considering the possibility that insertion and
deletion events can occur, significantly increases
the number of possible alignments between pairs
of sequences
For example, the two sequences AATCTATA and
AAGATA that can be aligned without gaps in only
three ways, admit 28 different alignments, with
the insertion of two gaps within the shorter
sequence
Example
AATCTATA
AAGATA
AATCTATA
AAGATA
AATCTATA
AAGATA
14
Simple penalties for gaps’ insertion
Introduction, in the alignment evaluation score, of
a penalty term for a gap insertion (gap penalty)
Penalty for a gap insertion, if seq1i“” o seq2i “”
Correspondence score, if seq1iseq2i
{
n
i1
Noncorrespondence score, if seq1iseq2i
Assuming a score of nomatching/matching equal
to 0/1 and a gap penalty equal to 1, the scores for
the three alignments with gaps (out of 28) would be
1, 3, 3
AATCTATA
AAGATA
AATCTATA
AAGATA
AATCTATA
AAGATA
15
Penalties for the presence and the length of a gap  1
Using a simple gap penalty, it is common to evidence
many “optimal” alignments (depending on the chosen
criterion)
Choose different penalty values for single gaps and gaps
that appear in sequence
Concretely, any pairwise alignment represents a
hypothesis about the evolutionary path that the two
sequences have undertaken from the last common
ancestor
When considering several competing hypotheses, the
one that invokes the fewest number of improbable
events is, by definition, the most probably correct
16
Penalties for the presence and the length of a gap  2
Let s1 and s2 be two arbitrary DNA sequences of length
12 and 9, respectively
Each alignment will necessarily have three gaps in the shorter
sequence
Assuming that s1 and s2 are homologous sequences, the
difference in length can be caused by the insertion of
nucleotides in the longer sequence, or by the deletion of
nucleotides in the shorter sequence, or by a combination of the
two events
Since the sequence of the ancestor is unknown, no methods
exist able to determine the cause of a gap, which is attributed
generally to an indel event (insertion/deletion)
Moreover,
since multiple
insertions/deletions are not
uncommon, it is statistically more likely that the difference in
length between the two sequences was due to a single indel of
3 nucleotides, rather than to many distinct indels
17
Penalties for the presence and the length of a gap  3
The scoring function has to reward alignments that are
most likely from the evolutionary point of view
By assigning a penalty on the length of the gap (which
depends on the number of sequential characters
missed) lower than the penalty for the creation of new
gaps, the scoring function rewards the alignments that
have sequential gaps
Example: using a gap creation penalty equal to 2, a
length penalty of 1 (for each gap), and nomatching/
matching values equal to 0/1, the scores in the three
cases below are respectively 3, 1, 1
AATCTATA
AAGATA
AATCTATA
AAGATA
AATCTATA
AAGATA
18
Score matrices  1
Just as the gap penalty, that can be adapted to reward
alignments evolutionarily more plausible, so the
nomatching penalty can be made nonuniform, based
on the simple observation that some substitutions are
more common than others
Example: let us consider two protein sequences, one
of which has an alanine at a given position
A substitution with another small and hydrophobic amino
acid, such as valine, has a lower impact on the resulting
protein with respect to a replacement with a large and
charged residue such as, for example, lysine
19
Score matrices  2
Alanine
Valine
Lysine
20
Score matrices  3
Intuitively, a conservative substitution, unlike a more drastic
one, may occur more frequently, because it preserves the
original functionality of the protein
Given an alignment score for each possible pair of
nucleotides or residues, the score matrix is used to assign a
value to each position of an alignment, except gaps
Example
Nucleotides’ matches are moderately
rewarded, while a small penalty is given to
transition events (substitution between
purines/pyrimidines, A-G/C-T); instead, a
more severe penalty is assigned for
transversions, in which a purine replaces a
pyrimidine or vice versa
A
A
T
1
5 5 1
T 5
1
C 5 1
C
G
1 5
1
5
G 1 5 5
1
21
Score matrices  4
Several criteria can be considered in setting up a
scoring matrix for amino acid sequence alignments
Physicochemical similarity
Observed replacement frequencies
In similarity based matrices, the coupling of two
different amino acids, which, however, have both
functional aromatic groups (hydrophobic amino acids,
characterized by a side chain containing a benzene
ring, such as phenylalanine, tyrosine and tryptophan)
could receive a positive score, while the coupling of
nonpolar with charged amino acids could be penalized
22
Score matrices  5
Score matrices can be derived according to the
hydrophobicity, the presence of charge, the
electronegativity, and the size of the particular
residue
Alternatively, similarity criteria based on the
encoding genome can also be used: the assigned
score is proportional to the minimum number of
nucleotide substitutions necessary to convert a
codon to another
Difficulty in combining, in a single “significant”
matrix, chemical, physical and genetic scores
23
Score matrices  6
The most common method to derive score
matrices consists in observing the actual
frequencies of amino acid substitutions in Nature
If a replacement which involves two particular
amino acids is frequently observed, their
alignment obtains a favorable score
Vice versa, alignments between residues which,
during evolution, are rarely observed must be
penalized
24
PAM matrices  1
PAM matrices exploit the concept of Point (or Percent)
Accepted Mutation; they were proposed in 1978, by M.
Dayhoff et al., on the basis of a study on molecular
phylogeny involving 71 protein families
PAM matrices were developed by examining mutations
within superfamilies of closely related proteins, also
noting how observed substitutions did not happen at
random
Some amino acid substitutions occur more frequently
than others, probably because they do not significantly
alter the structure and the function of a protein
Homologous proteins need not to be necessarily
constituted by the same amino acids in each position
25
PAM matrices  2
Two proteins are “distant” 1 PAM unit if they differ
for a single amino acid out of 100, and if the
mutation is accepted, i.e. it does not result in a
loss of functionality
In other words… two sequences s1 and s2 are distant
1 PAM if s1 can be transformed into s2 with a point
mutation per 100 amino acids, on average
Since the amino acid at a certain position may
change several times and then may return to the
original character, the two sequences that are 1
PAM may differ by less than 1%
26
PAM matrices  3
Examples of this type of protein families collect
orthologous proteins (which perform the same
function
in
different
organisms);
instead,
pathological changes, that are associated to loss
of functionality, do not belong to this class
To generate a PAM 1 matrix, we consider a pair
(or more) of very similar protein sequences (with
an identity 85%), for which the alignment can be
defined without ambiguity
27
PAM matrices  4
Based on this set of proteins, a PAM 1 score matrix
can be defined as follows:
Calculation of an alignment among sequences with very
high identity
For each pair of amino acids i and j, calculation of Fij, the
number of times that the amino acid j is replaced by i
For each amino acid j, evaluation of the relative
mutability nj (the number of substitution of such amino
acid, appropriately normalized)
Evaluation of Mij, the mutation probability for each
amino acid pair j  i
Finally, each PAM 1 element, Pij, is evaluated by applying
the logarithm to Mij, previously normalized w.r.t. the
frequency of the residue i (PAM 1 is also called the
logodds matrix)
28
PAM matrices  5
Example (to be continued)
1) Construction of a multiple sequence alignment:
ACGCTAFKI
GCGCTAFKI
ACGCTAFKL
GCGCTGFKI
GCGCTLFKI
ASGCTAFKL
ACACTAFKL
29
PAM matrices  6
Example (to be continued)
2) A phylogenetic tree is created, that indicates the order
in which substitutions may have been occurred during
evolution
ACGCTAFKI
AG
GCGCTAFKI
AG
GCGCTGFKI
AL
GCGCTLFKI
IL
ACGCTAFKL
CS
ASGCTAFKL
GA
ACACTAFKL
30
PAM matrices  7
Example (to be continued)
3) For each amino acid, we calculate the number of
replacements with respect to any other amino acid
It is assumed that the substitutions are symmetric, that is
they occur with the same probability with respect to a
given pair of amino acids
For instance, in order to determine the substitution
frequency between A and G, FG,AFA,G, we count all the
branches AG and GA
FG,A 3
31
PAM matrices  8
Example (to be continued)
4) Calculation of the relative mutability
acid
nj of each amino
The mutability mj is the number of times an amino acid is
replaced by any other in the phylogenetic tree
This number is then normalized by the total number of
mutations that may have some effects on the residue
...that is, the denominator of the fraction is given by the
total number of substitutions in the tree, multiplied by
two, multiplied by the frequency of the particular amino
acid, multiplied by a scale factor equal to 100
The scale factor 100 is used because the PAM 1 matrix
represents the substitution probability per 100 residues
32
PAM matrices  9
Example (to be continued)
Let us consider the amino acid A (alanine): there are 4
mutations involving A in the phylogenetic tree (mA 4)
This value must be divided by twice the total number of
mutations (6212), multiplied by the relative frequency
of the residue fA (10630.159), multiplied by 100
nA4(120.159100)0.0209
33
PAM matrices  10
Example (to be continued)
5) Let us calculate the mutation probability
pair of amino acids
Mij, for each
MijnjFij/jFij
and then…
MG,A(0.02093)40.0156
where the denominator jFij represents the total
number of substitutions that involves A in the
phylogenetic tree
34
PAM matrices  11
Example
6) Finally, each
Mij must be divided by the frequency of
the residue i; the logarithm of the resulting value
constitutes the corresponding element of the PAM
matrix, Pij
For G, the frequency fG is equal to 0.159 (1063)
For G and A, PG,Alog(0.01560.159)1.01
7) By repeating the above procedure for each pair of
amino acids we can obtain all the extradiagonal
values of the PAM matrix, whereas Pii are calculated
posing Mii 1ni and executing 6)
35
PAM matrices  12
High order PAM matrices are generated by successive
multiplications of the PAM 1 matrix, since the
probability of two independent events is equal to the
product of the probabilities of each individual event
While for the PAM 1 matrix it holds that a mutational
event corresponds to a difference of 1%, this is not
true for higher order PAM matrices
Indeed, subsequent mutations have a gradually
increasing chance to happen in correspondence of
already mutated amino acids
The degree of difference increases with the increase in
the number of mutations, but while it can tend to
infinity, the difference tends asymptotically to 100%
36
PAM matrices  13
The choice of the most suitable PAM matrix with respect to a
particular alignment of sequences, depends on their length
and on their correlation degree
PAM 2 is calculated from PAM 1 assuming another
evolutionary step
PAM n is obtained from PAM n1
PAM 100, therefore, represents 100 evolutionary steps, in
each of which there was a 1% of substitutions more
compared to the previous step
phylogenetically
close sequences
PAM 1
PAM 100
phylogenetically
distant sequences
PAM 250
37
PAM matrices  14
PAM 250 matrix
38
PAM matrices  15
It is worth noting that:
Each PAM matrix element Pij describes how much
the substitution of the amino acid Aj with the amino
acid Ai is more (or less) frequent that a random
mutation
Therefore:
Pij  0 more frequent than a random mutation
Pij  0 frequent as a random mutation
Pij  0 less frequent than a random mutation
39
BLOSUM matrices  1
The BLOSUM matrices (BLOcks amino acid SUbstitution
Matrices) were introduced in 1992 by S. Henikoff and J. G.
Henikoff to assign a score to substitutions between amino
acid sequences
Their purpose was to replace the PAM matrices, making use
of the increased amount of data that had become available
after the work of Dayhoff
They were supposed to work better than PAMs especially
with respect to poorly correlated sequences
The BLOCKS database contains multiply aligned ungapped
segments corresponding to the most highly conserved
regions of proteins
Each alignments’ block contains sequences with a number of
identical amino acids grater than a certain percentage N
From each block, it is possible to derive the relative
frequency of amino acid replacements, which can be used to
calculate a score matrix
40
BLOSUM matrices  2
The elements of the BLOSUM matrix, Bij, are evaluated
based on the following relation
Bij = klog(M(Ai,Aj)/C(Ai,Aj)), k costant
– M(Ai,Aj) is the substitution frequency of the amino acid Aj
with the amino acid Ai, observed in the group of the
considered homologous proteins
– C(Ai,Aj)
is the expected substitution frequency,
represented by the product of the frequencies of amino
acids Ai and Aj in all the groups of the considered
homologous proteins
Even in this case, the matrix element (i,j) is
proportional to the substitution frequency of the amino
acid Aj with the amino acid Ai
phylogenetically
distant sequences
phylogenetically
close sequences
41
BLOSUM35
BLOSUM62
Example: BLOSUM62
42
PAM or BLOSUM  1
The two types
assumptions
of
matrices
start
from
different
For PAM matrices, it is assumed that the observed amino
acid substitutions for large evolutionary distances derive
solely by the summing of many independent mutations;
the resulting scores express how likely it is that the
pairing of a particular couple of amino acids is due to
homology rather than to randomness
The BLOSUM matrices are not explicitly based on an
evolutionary model of mutations; each block is obtained
from the direct observation of a family of related proteins
(so probably also evolutionarily related), but without
explicitly evaluate their similarity
43
PAM or BLOSUM  2
An increasing PAM index describes a suitable score for
“distant” proteins, expressing also an evolutionary
distance; instead, an increasing BLOSUM index
represents a suitable score for protein similar to each
others, expressing the minimum conservation value for
the BLOCK
PAM matrices tend to reward amino acid substitutions
resulting from single base mutations, also penalizing
substitutions involving more complex changes in the
codons; instead, they do not reward structural amino
acid motifs, as the BLOSUMs do
44
PAM or BLOSUM  3
The comparison between PAM and BLOSUM, to a
comparable level of substitutions, indicates that the
two types of matrices produce similar results
Typically, the BLOSUM matrices are deemed most
suitable to search for sequence similarity
The BLOSUM62 matrix is normally set as the default in
the similarity search software
In any case, it is important to choose the most
suitable matrix based on the phylogenetic distance
between the sequences to be compared
For phylogenetically close sequences (and organisms)
low index PAM or high index BLOSUM must be chosen
For phylogenetically distant sequences, high index
PAM or low index BLOSUM are suitable
45
Dynamic Programming:
The Needleman-Wunsch algorithm  1
Once having selected a method for assigning a score
to an alignment, it is necessary to define an algorithm
to determine the best alignment(s) between two
sequences
The exhaustive search among all possible alignments
is generally impractical
For two sequences, respectively 100 and 95 nucleotide long,
there are 55 million possible alignments, just only in the case
of five gaps inserted in the shorter sequence
The exhaustive search approach becomes rapidly
intractable
Using dynamic programming, the problem can be divided into
subproblems of more “reasonable” size, whose solutions must
be recombined to form the solution of the original problem
46
Dynamic Programming:
The Needleman-Wunsch algorithm  2
S. B. Needleman and C. D. Wunsch, in 1970, were the
first who solved this problem with an algorithm able to
find global similarities, in a time proportional to the
product of the lengths of the two sequences
The key for understanding this approach is to observe
how the alignment problem can be divided into
subproblems
47
Dynamic Programming:
The Needleman-Wunsch algorithm  3
Example (to be continued)
Align CACGA and CGA with the assumption of uniformly
penalizing gaps and mismatches
Possible choices to be made with respect to the first
character:
1) Place a gap in the first place of the first sequence
(counterintuitive, given that the first sequence is longer)
2) Place a gap in the first place of the second sequence
3) Align the first two characters
In the first two cases, the alignment score for the first
position will be equal to the gap penalty
In the third case, the alignment score for the first
position will be equal to the match score
The rest of the score will depend, in all the cases, on the
way in which the remaining part of the two sequences
will be aligned
48
Dynamic Programming:
The Needleman-Wunsch algorithm  4
Example (to be continued)
First position
Score
Sequences to be aligned
C
C
1
ACGA
GA

C
1
CACGA
GA
C

1
ACGA
CGA
If we knew the score for the best alignment between the
remaining parts of the sequences, we could easily
calculate the best overall score relative to the three
possible choices
49
Dynamic Programming:
The Needleman-Wunsch algorithm  5
Example
Starting from the assumption of aligning the two initial
characters (without inserting gaps), it remains to
calculate the alignment score for the sequences ACGA
and GA
In this operation, it will often be necessary to calculate
scores for subsequences (e.g.: ACGA and GA)
Dynamic programming is based on constructing a
table, in which the partial alignment scores are stored,
in order to avoid to recalculate them many times
50
Dynamic Programming:
The Needleman-Wunsch algorithm  6
The dynamic programming algorithm computes the
optimal alignment between sequences filling a table
with partial scores
The horizontal and vertical axes describe, respectively,
the two sequences to be aligned
Example: table for the
alignment of ACAGTAG and
ACTCG, with a gap penalty
of 1 and a score of mis/
matching equal to 0/1
A
0
A
1
C
2
A
3
G
4
T
5
A
6
G
7
C
T
C
G
1 2 3 4 5
51
Dynamic Programming:
The Needleman-Wunsch algorithm  7
The alignment of the two sequences is equivalent to
build a path that goes from the upper left to the lower
right corner of the table
A horizontal shift represents a gap inserted in the
vertical sequence and vice versa
Moving along the diagonal means aligning the
corresponding nucleotides in the two sequences
The first row and the first column of the table are
initialized with multiples of the gap penalty (in fact,
each gap adds a penalty to the total alignment score)
52
Dynamic Programming:
The Needleman-Wunsch algorithm  8
How can we calculate the other elements of the table?
The element in position (2,2) is calculated by exploring the
following three possibilities:
1)
2)
3)
Adding up the gap penalty to the entry in position (2,1),
which corresponds to consider a gap in the vertical sequence
Adding up the gap penalty to the entry in position (1,2),
which corresponds to consider a gap in the horizontal
sequence
Adding up the mis/match score to the entry in the diagonal
position (1,1), which corresponds to the alignment of the
related nucleotides
The maximum value among those obtained for the three
options (2,2,1) is then assigned to the element in position
(2,2)
53
Dynamic Programming:
The Needleman-Wunsch algorithm  9
We can then proceed to fill the entire second row, then
move on to the next row, up to complete the table
A
C
T
C
G
0
1 2 3 4 5
A
1
1
0
1 2 3
C
2
0
2
1
0
1
A
3
1
1
2
1
0
G
4
2
0
1
2
2
T
5
3 1
1
1
2
A
6
4 2
0
1
1
G
7
5 3 1
0
2
Example
N(3,5)  max{(11),(11),(21)}
 max{0,0,3)}  0
54
Dynamic Programming:
The Needleman-Wunsch algorithm  10
After completing the table, the value in the lower right
corner is the score for the optimal alignment between
the two sequences (2, in the example)
Remark: The score was determined without having to
assign a score to all the possible alignments between
the two sequences
The table of the partial scores allows to reconstruct
the optimal alignments (generally more than one)
between the two sequences
Tracing a path from the lower right to the upper left
position
55
Dynamic Programming:
The Needleman-Wunsch algorithm  11
Example
The value N(8,6)2 may have been obtained following three
different routes, but the only one that can produce a value
of 2 is that coming from N(7,5)1 (alignment of G in both
the sequences)
A
C T C G
Again, for the value N(7,5)
0 1 2 3 4 5
exists only one possibility,
which leads to the element A 1 1 0 1 2 3
N(6,4)1 (with 0 mismatch C 2 0 2 1 0 1
score
between
the
two A 3 1 1 2 1 0
nucleotides)
G
4 2 0 1 2 2
The
process
must
be
T
5 3 1 1 1 2
repeated until all the possible
paths are completed, to A 6 4 2 0 1 1
G
7 5 3 1 0 2
reach the final position (1,1)
56
Dynamic Programming:
The Needleman-Wunsch algorithm  12
If n and m represent the lengths of the two sequences
to be aligned, to convert a path in an alignment, each
path from (n1,m1) to (1,1) must be traveled
backwards, recalling that:
a vertical movement represents a gap in the sequence
along the horizontal axis
a horizontal movement represents a gap in the sequence
along the vertical axis
a diagonal movement represents an alignment of the
nucleotides, belonging to the two sequences, at the
current position
57
Dynamic Programming:
The Needleman-Wunsch algorithm  13
Example
G
G
CG
AG
TCG
TAG
TCG
GTAG
TCG
AGTAG
CTCG
CAGTAG
ACTCG
ACAGTAG
A
C
T
C
G
0
1 2 3 4 5
A
1
1
0
1 2 3
C
2
0
2
1
0
1
A
3
1
1
2
1
0
G
4
2
0
1
2
2
T
5
3 1
1
1
2
A
6
4 2
0
1
1
G
7
5 3 1
0
2
Remark: Following all the paths (n1,m1)(1,1)
in the table of the partial scores, all the possible
optimal alignments between the two sequences
can be reconstructed
58
The Needleman-Wunsch algorithm
Example  1
Alignment of the sequences CACGA and CGA
C
0
1
C
1
1
A
2
0
C
3
1
G
4
2
A
5
3
N(5,2)
N(5,3)
N(5,4)
N(6,2)
N(6,3)
N(6,4)






G
A
N(2,2)  max{(11),(11),(01)}  max{2,2,1)}  1
2 3 N(2,3)  max{(11),(21),(10)}  max{0,3,1)}  0
0 1 N(2,4)  max{(01),(31),(20)}  max{1,4,2)}  1
N(3,2)  max{(21),(11),(10)}  max{3,0,1)}  0
1 1
N(3,3)  max{(01),(01),(10)}  max{1,1,1)}  1
0 1 N(3,4)  max{(11),(11),(01)}  max{0,2,1)}  1
0 0 N(4,2)  max{(31),(01),(21)}  max{4,1,1)}  1
N(4,3)  max{(11),(11),(00)}  max{2,0,0)}  0
1 1
N(4,4)  max{(01),(11),(10)}  max{1,0,1)}  1
max{(41),(11),(30)}  max{5,2,3)}  2
max{(21),(01),(11)}  max{3,1,0)}  0
max{(01),(11),(00)}  max{1,0,0)}  0
max{(51),(21),(40)}  max{6,3,4)}  3
max{(31),(01),(20)}  max{4,1,2)}  1
max{(11),(01),(01)}  max{2,1,1)}  1
59
The Needleman-Wunsch algorithm
Example  2
Alignment of the sequences CACGA and CGA
C
G
A
0
1 2 3
C
1
1
0
1
A
2
0
1
1
C
3
1
0
1
G
4
2
0
0
A
5
3 1
1
 Two admissible paths
Two optimal alignments with score equal to 1
CGA
CACGA
CGA
CACGA
60
Global and local alignments  1
Global alignment: obtained by trying to align the maximum
number of characters between the two sequences; ideal
candidates are sequences of similar length
Local alignment: obtained by trying to align “pieces” of
sequences with a high degree of similarity; the alignment
terminates when “the island of coupling” ends; ideal
candidates are sequences with significantly different
lengths, which contain highly conserved regions
61
Global and local alignments  2
The
Needleman-Wunsch
algorithm
performs
global
alignments, i.e. it compares sequences in their entirety
The gap penalty is fixed, without weighing the gap position
(located inside or at the ends of sequences)
It is not always the best way to perform the alignment
Example: let us suppose to search for an occurrence of the
short subsequence ACGT within the longer sequence
AAACACGTGTCT (this is a pattern matching approach)
Among several possibilities, the alignment of interest is:
AAACACGTGTCT
ACGT
When searching for the best alignment between a short
sequence and a whole genome (to isolate a gene, for
instance), penalizing the gaps that appear at one or both the
ends of a sequence should be avoided
62
Global and local alignments  3
The final gaps are usually the result of an incomplete data
acquisition and have no biological significance
it is appropriate to treat them differently from internal gaps
semiglobal alignment
How can we change the dynamic programming algorithm to
wire this new behavior?
With the Needleman-Wunsch algorithm, for the sequences
ACTCG and ACAGTAG, we can first move vertically towards the
bottom row of the table, and then horizontally to the last
column, until we reach the last entry, obtaining:
ACTCG
ACAGTAG
63
Global and local alignments  4
Indeed, from the upper left of the table, each downward
movement adds an additional gap in the alignment at the
beginning of the first sequence...
...and, since each gap adds a gap penalty to the total score
of the alignment, the first column is initialized with the gap
penalty multiples
Conversely, if we want to allow the presence of initial gaps
in the first sequence without assigning any penalty
The first column entries should be set to zero
Likewise, initializing the first row of the table with all zeroes,
we allow the presence of initial gaps in the second sequence
without assigning penalty
64
Global and local alignments  5
To admit no penalty gaps at the end of a sequence, the
meaning of some movement within the table must be
differently reinterpreted
Example: Let us suppose to have the following alignment:
ACACTGATCG
ACACTG 
Using the alignment to build a path in the table of partial
scores, after aligning the first six nucleotides, we reach the
bottom row
Then, to reach the lower right corner, we should perform four
horizontal movements
Allow horizontal movements in the last row without assigning a
gap penalty
Similarly, vertical movements on the last column should not be
penalized
65
Global and local alignments  6
A
C
A
C
T
G
A
T
C
G
0
0
0
0
0
0
0
0
0
0
0
A
0
1
0
1
0
0
0
1
0
0
0
C
0
0
2
1
2
1
0
0
1
1
0
A
0
1
1
3
2
2
1
1
0
1
1
C
0
0
2
2
4
3
2
1
1
1
1
T
0
0
1
2
3
5
4
3
2
1
1
G
0
0
0
1
2
3
6
6
6
6
6
66
Global and local alignments  7
In summary:
By initializing the first row and the first column of the
table with all zeroes…
…and allowing nonpenalized horizontal and vertical
movements, respectively, in the last row and in the last
column of the table
A semiglobal alignment is performed
Unfortunately, not even semiglobal alignments offer a
sufficient flexibility to address all the possible issues
related to sequence alignments
67
The Smith-Waterman algorithm  1
In 1981, T. F. Smith and M. S. Waterman developed a
new algorithm capable of detecting also local similarity
Example: Let us suppose to have a long DNA sequence
and want to isolate each subsequence similar to each
part of the yeast genome
A semiglobal alignment is not sufficient because it will
however penalize each noncorrespondence position
Even if there were an interesting subsequence, partly
coincident with the yeast genome, all noncorrespondent
nucleotides will contribute to generate an unsatisfactory
alignment score
Local alignment
68
The Smith-Waterman algorithm  2
Example: Let us consider the two sequences AACCTATAGCT
and GCGATATA
By using a semiglobal alignment with a 1 gap penalty and
non/correspondence scores equal to 1/1, we will obtain the
following alignment:
AACCTATAGCT
GCAATATA
which is pretty poor, given that four of the top five positions
are mismatches or gaps, as well as the last three positions
However, there is a “correspondence region” within the two
sequences: the TATA subsequence
Change the algorithm in order to identify matches between
subsequences, ignoring mismatches and gaps before and after
the region of correspondence
69
The Smith-Waterman algorithm  3
For the local alignment of two sequences:
Initialize the first row and the first column to zero (as in
the semiglobal alignment)
Set the mismatch penalty to 1
Enter a zero entry in the table wherever all the other
routes return a negative score
After having built the table:
Find the maximum partial score
Proceed backwards, to rebuild the alignment, until a zero
entry is reached
The resulting local alignment represents the best
matching subsequence between the two given
sequences
70
The Smith-Waterman algorithm  4
A
A
C
C
T
A
T
A
G
C
T
0
0
0
0
0
0
0
0
0
0
0
0
G
0
0
0
0
0
0
0
0
0
1
0
0
C
0
0
0
1
1
0
0
0
0
0
2
1
G
0
0
0
0
0
0
0
0
0
1
1
1
A
0
1
1
0
0
0
1
0
1
0
0
0
T
0
0
0
0
0
1
0
2
1
0
0
1
A
0
1
1
0
0
0
2
1
3
2
1
0
T
0
0
0
0
0
1
1
3
2
2
1
2
A
0
1
1
0
0
0
2
2
4
3
2
1
In summary… when working with long sequences, of several
thousands, or millions, of nucleotides, local alignment
methods can identify common subsequences, impossible to
be found by means of global or semiglobal alignments
71
Biological data  1
1965: Margaret Dayhoff defines an atlas of
homologous
proteins,
studying
the
relationships
among
their
primary
sequence;
the
collected
data
were
distributed in 1970, in the database NBRF
(National Biomedical Research Foundation)
Early
‘70s:
The
recombinant
DNA
technology (fundamental for cloning) is
established, which allows the manipulation
of the nucleotide sequences, guaranteeing
the comprehension of the DNA structure,
function and organization
Late ‘70s: Publication of the first genomic
data (F. Sanger), with a small number of
nucleotide encoding sequences, freely
accessible via the network (restricted to
few universities)
72
Biological data  2
1980 [Kurt Stueber]: Birth of the first genomic database,
at the European Molecular Biology Laboratory (EMBL) in
Heidelberg
1982 [Walter Goad]: Birth of a similar database in the
USA, which will converge later in GenBank
1986: A mirror of GenBank, DDBJ (DNA DataBank of
Japan), was set up at the National Institute of Genetics in
Mishima (Japan)
2001: The International Public Consortium and Celera
Genomics provide the complete human genome
73
Biological databases  1
Molecular biotechnology developments have led to
the production of a huge amount of biological
data
Biological databases are designed as containers,
constructed to store data in an efficient and
rational way, and to make them easily accessible
to the users
Their ultimate goal consists in collecting and
analyzing data, based on ad hoc tools available
within each database
74
Biological databases  2
Numerous biological databanks exist today:
Primary Databanks
Nucleotide and amino acid sequences
Specialized databanks
Genes
Protein structures
Protein domains and motifs  protein domains are compact
semiindependent regions with distinctive functions, linked
to the rest of the protein by a portion of the polypeptide
chain that serves as a hinge
Transcriptome expression profiles  transcriptome (a term
analogous to genome, proteome or metabolome) means
the set of all transcripts (messenger RNA or mRNA) of a
given organism or cell type
Metabolic pathways  a metabolic pathway (or simply a
pathway) is the set of chemical reactions involved in one or
more processes of anabolism or catabolism within a cell
…
75
Biological databases  3
Biological databases
derived from:
collect information and
data
the literature
laboratory analyses (in vitro and in vivo)
bioinformatic analyses (in silico)
Many biological databases are freely downloadable in
flat format, i.e. in the form of sequential file in which
each record is described by one or more consecutive
text lines, identified by a particular unique code
These files are therefore text files, that can be
analyzed by means of suitable tools, able to extract
the information of interest
Alternative: data in HTML or XML format, easy to be
consulted via browsers
76
Biological databases  4
Each database is characterized by a central biological
element that constitutes the object around which the
database records are built
Therefore, each record collects the information that
characterizes the central element (i.e., its attributes)
A record of a DNA database may contain, in addition
to the sequence of a DNA molecule,
the name of the organism to which the sequence
belongs
a list of scientific papers reporting data on that sequence
its functional characteristics (i.e., if it corresponds to a
gene or a to a noncoding sequence)
other interesting information
77
Biological databases  5
Biological databases provide bioinformatics tools
for processing the data they contain, including:
Query systems (ENTREZ, associated with GenBank,
SRS, for EMBL, DBGET, for DDBJ)
Screening tools (BLAST, FASTA)
Multiple sequence alignment tools (ClustalW,
AntiClustal, TCoffee, ProbCons)
Tools for the identification of exons and regulatory
elements that characterize a gene (GenScan,
Promoser)
…
78
Primary biobanks  1
Primary databases contain nucleotide (DNA and RNA)
or amino acid (protein) sequences
The main primary databases are:
GenBank (NCBI  National Center for Biotechnology
Information, founded in 1982 in Bethesda, USA,
http://www.ncbi.nlm.nih.gov);
the standard database
contains
187.893.826.750
bases
belonging
to
181.336.445 sequences (February 2015)
EMBL datalibrary (founded in 1980 at EMBL  European
Molecular Biology Laboratory, in Heidelberg, Germany,
http://www.embl.de)
DDBJ (DNA DataBase of Japan, constituted in 1986 by
the National Institute of Genetics in Mishima, Japan,
http://www.ddbj.nig.ac.jp/index-e.html)
79
Primary biobanks  2
Among the three main biological databanks, an
international agreement has been established to
ensure that DNA data are kept consistent (daily
updates made in each bank are automatically
transferred to the others)
Moreover, the three institutions cooperate to
share and make publicly available all the data
they collect, that differ only in the format in which
they are released
80
NCBI  1
The Agc1 deficit is a neurodegenerative syndrome that
causes a reduction of the
content of myelin, the sheath
surrounding nervous cells in
the brain. Since the very first
months of life, it implies
severe psychomotor problems,
seizures and difficulties in
breathing and in movements
controlling.
81
NCBI  2
NCBI is a database of genetic sequences, owned by
the USA National Institute of Health; it contains an
annotated collection of all publicly available DNA
sequences
Access to data through ENTREZ, the query system
used for all the different databases managed by NCBI,
which therefore constitutes a complete hub to search
for information
Available via web, for the search and the extraction of
information from databases of nucleotide and protein
sequences, from the bibliographic database PubMed, the
database of Mendelian diseases OMIM, and any database
developed by NCBI
Closed system: the software that runs the system
cannot be downloaded
82
NCBI  3
Main databases in NCBI:
Gene: It contains data related to the genes of all the
characterized species, such as gene structure and
genomic context, ontologies, interactions with other
genes and links to related sequences and scientific
publications
Nucleotide: It contains the nucleotide non/coding
sequences of all the characterized species
Protein: It shares the same structure of Nucleotide, but
it contains amino acid sequences
PubMed: It is the database of scientific biological and
biomedical publications; the abstract is available for
each paper; PubMed Central contains fulltext articles
available for free download
83
NCBI  4
Entrez also provides the possibility to make
crosssearching, for collecting information from the
various NCBI databases (sequencestructuregenetic
mapliterature)
84
Protein databanks  1
Protein sequences
following ways:
may
be
obtained
in
the
Directly determining the protein sequence
Translating the nucleotide sequences for which the
function of the encoding gene has been identified
or predicted
Studying gene expressions
Via crystallography, by the determination of
secondary and tertiary structures
85
Protein databanks  1
SWISS-PROT
(Protein
knowledgebase,
1986):
reference database developed in Geneve (Switzerland); it contains carefully annotated information
(often handmade)
TrEMBL (Translated EMBL): it results from the
automatic translation  into amino acid sequences  of
all the DNA sequences belonging to the EMBL database
and annotated as encoding proteins; supplementary to
SWISS-PROT
PIR (Protein Information Resource): mainly devoted to
define the annotation standards
TrEMBL and PIR together formed the UniProt
consortium, the centralized repository of all the protein
sequences
86
Specialized databases
Specialized databases have been developed later
They collect sets of homogeneous data from the
taxonomic and/or functional point of view, available in
primary databases and/or in literature, or derived from
experimental approaches, revised and annotated with
more information
Examples:
wwPDB (world wide Protein Data Bank), the reference
database for 3D protein data, equipped with the atomic
coordinates determined through Xray cristallography, NMR
analysis, etc.
Database of genomic sequences: GDB (man), MGI (mouse),
SGD (yeast)
Database of genes and transcripts: UniGene, LocusLink, dbEST,
etc.
87
Database search  1
Sequence alignments can be a valuable tool for
comparing two known sequences
A more common use of alignments, however, consists
in the search within a database, containing biological
data, of the sequences that are similar to a particular
sequence of interest
The search results, which consists of other sequences
that align well with (and thus are similar to) the query
sequence, may in fact provide:
a suggestion on the functional role of the sequence at
hand
some clues about its regulation and expression in
connection with similar sequences in other species
88
Database search  2
Example:
sequencing of a part of the human genome that could
constitute a gene not previously identified
comparison of the “putative” gene with millions of
sequences deposited in the database GenBank at the
NCBI
During searching in a biological database, both the
size of the database and of the individual data often
preclude the obvious approach to align the query
sequence to all other sequences, in order to obtain the
highest alignment scores
Special indexing and search techniques, guided by
heuristics, are normally employed
89
Database search  3
Most of the commonly used algorithms do not
guarantee to obtain the maximum, but they do
provide some statistical confidence on the retrieval of
the majority of the sequences that align well with the
query sequence
BLAST (Basic Local Alignment Search Tool)
FASTA (FastAll, an extension of FASTN and FASTP,
respectively dedicated to alignments in nucleotide and
polypeptide chains)
The efficiency is a prerequisite and a fundamental
feature for these bioinformatics methods, which have
become of essential support to molecular biology
90
BLAST and its variants
Probably the most popular and commonly used tool to
search for sequences in biological databases is BLAST,
introduced by S. Altschul et al. in 1990
BLAST looks for long local alignments without gaps, i.e. it
detects subsequences belonging to the database similar to
subsequences of the query sequence
BLAST can run thousands of comparisons between
sequences in few minutes and, in a short time, a query
sequence can be compared with the entire database to
search for all the similar sequences
There are different variants and versions of BLAST, to search
for nucleotide and protein sequences
BLASTN, BLASTP, BLASTX, TBLASTN
Nucleotide), BLAST 2.0, PSIBLAST
(Translated
BLAST
91
BLASTN
It searches for correspondences among nucleotide
sequences, using the simple score matrix:
A
T
C
G
A
5
4
4
4
T
4
5
4
4
C
4
4
5
4
G
4
4
4
5
with
uniform
penalties
for
transitions
and
transversions, in order to assign scores to alignments
without gaps
92
BLASTP  1
It searches for correspondences of protein
sequences, using PAM or BLOSUM matrices to
assign a score to alignments without gaps
It divides the query sequence into words, or
subsequences, of fixed length (4 being the default
length)
It uses a sliding window, with size equal to the
word length, along the entire sequence
Example: the query sequence AILVPTV produces four
different words  AILV, ILVP, LVPT, VPTV
The words consisting mainly of common amino
acids are not considered for searching
The remaining words are searched in the database
93
BLASTP  2
When a correspondence is found, the matched
subsequence is extended in both the directions until the
alignment score drops below a given threshold
The extension corresponds to the addition of new residues
to the matching subsequence with the recalculation of the
alignment score in accordance with the scoring matrix
The choice of the threshold value is an important
parameter because it determines the probability that the
resulting sequences are biologically relevant counterparts
of the query sequence
Example: Search for AILVPTV
AILV
MVQGWALYDFLKCRAILVGTVIAML…
AILVPTV
MVQGWALYDFLKCRAILVGTVIAML…
94
BLAST and its variants (cont.)
Numerous algorithms for sequence alignment and database
search have been developed for specific types of data
BLASTN, BLASTX allow, respectively, to search in nucleotide
databases and to translate the nucleotide sequence into the
protein sequence before searching
TBLASTN compares the query protein with the nucleotide
sequence database; in order to make this kind of comparison,
the database sequences are dynamically translated into amino
acid sequences and then compared with the query protein
BLAST 2.0 inserts gaps to optimize the alignment
PSIBLAST summarizes the search results into scoring,
positiondependent matrices, useful in detecting remote
homologous, and for modeling and predicting the protein
structure
95
FASTA and its variants  1
FASTA algorithms constitute a different family of
alignment and search tools
They perform local alignments with gaps between
sequences of the same type
They are more sensitive than BLASTlike algorithms,
especially for repetitive query sequences
They are computationally more expensive
Also in this case the sequence is divided into words
of length 46 for genomic sequences
of length 12 for polypeptide sequences
Successively, a table for the query sequence is
constructed, that shows the positions of each word
within the sequence
96
FASTA and its variants  2
Example (to be continued)
Let us consider the amino acid sequence
FAMLGFIKYLPGCM
which, for a word of length 1, produces the following table:
A C D E F G H I K L
M N P Q R S T V W Y
2
4
3
10
14
13
1
5
6
12
7
8
11
9
The column relative to phenylalanine (F) contains the
values 1 and 6, which correspond to the positions of F in the
query sequence
97
FASTA and its variants  3
Example (to be continued)
To compare the query sequence with the target sequence
TGFIKYLPGACT, a second table is built, with respect to the latter
sequence, that correlates the respective positions of the amino
acids
1
2
3
4
5
6
7
8
9 10 11 12
T
G
F
I
K
Y
L
P
G
A
C
3
2
3
3
3
3
3
4
8
2
10
3
3
T
3
Let us consider the position 2, relative to the glycine residue (G)
In the query sequence, G occupies the positions 5 and 12
The distances between 5 and 12 and the position of the
first G in the target sequence (2) produce the two values 3
and 10
Similarly, in correspondence of the second G in position 9,
98
we obtain the values (59)4 e (129)3
FASTA and its variants  4
Example
Amino acids that are not found in the query sequence, such
as threonine (T), have not assigned values (the columns in
the target table can be deleted)
The high number of elements with a distance equal to 3
suggests that a shifting of three positions to the left for the
query sequence (or of three positions to the right for the
target sequence) can produce a reasonable alignment
FAMLGFIKYLPGCM
TGFIKYLPGACT
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FASTA and its variants  5
Comparing the tables, after the ad hoc shift of one of
the sequence, the identity areas can be found quickly
These areas are then joined, to form longer
sequences, which are aligned using the SmithWaterman algorithm
However, since the alignment starts from a known
region within two similar sequences, FASTA is much
faster than the direct use of dynamic programming,
which implies to find a complete alignment between
the query sequence and all the possible targets
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Alignment scores  1
Although a database search will always produce a
result, without additional information, the extracted
sequences cannot always be considered to be related
with the query sequence
The alignment score is the main indicator of how much
the search results are similar to the query sequence
The alignment scores vary according to the particular
search tool
They do not represent, by themselves, an adequate
indicator to establish the actual (evolutionary)
correlation between the extracted sequences
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Alignment scores  2
If the search result gives an alignment score S, we can
then ask:
Given a set of sequences unrelated to the query sequence,
which is the probability to randomly find a match with an
alignment score equal to S?
To address this problem, search engines in biological
databases provide additional scores, known as E (or
Evalue) and P, for each output
E and P are different because:
E is proportional to the expected number of random
sequences with an alignment score  S
P represents the probability that the database contains one
or more random sequences with score  S
They are closely related and often they have “similar”
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values
Alignment scores  3
Small values for E and P indicate a very low probability
that the result of a search has been obtained casually
Values of E  103 are considered indicative of
statistically significant results
Often, the alignment algorithms provide results with E
 1050
There is a strong likelihood of evolutionary relationship
between the query sequence and the search results
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Multiple alignments  1
Multiple alignments are useful when observing a certain
number of “similar” sequences, for example to determine
the frequencies of substitution
A multiple alignment can summarize the evolutionary
history of a protein family
Therefore, we can obtain information about:
The conservation of residues dependent on the protein function
The conservation of residues dependent on the protein structure
Examples of functional/structural information that can be
obtained from a multiple alignment:
In enzymes, the most conserved regions probably correspond to
the active site
A conserved pattern of hydrophobic residues alternating with
hydrophilic residues suggests a sheet
A conserved pattern of hydrophobic residues every four residues
suggests the existence of an helix
Multiple alignments are also extremely useful for creating
score matrices, like PAM and BLOSUM
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Multiple alignments  2
An example of a multiple alignment among sequences
Evolutionary significance of a multiple alignment
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Multiple alignments  3
The simplest multiple alignment techniques are logical
extensions of the dynamic programming methods (like
Needleman-Wunsch)
In order to align n sequences an ndimensional grid is
needed
The computational complexity of multiple alignment
methods grows rapidly with the number of sequences to
be aligned
Even with a considerable computing power based on
massive parallelism, multiple alignments of more than
twenty sequences, of average length and complexity,
represent an intractable problem
Alignment methods guided by heuristics
Clustal
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Multiple alignments  4
The Clustal algorithm, proposed by Higgins and Sharp
in 1988, implements a progressive alignment, trying to
match closely related sequences first, and then adding
sequences with growing divergence
A phylogenetic tree is constructed to determine the
degree of similarity among the sequences to be aligned
Using the tree as a guide, closely related sequences are
aligned in pairs via dynamic programming, to reach the
complete multiple alignment
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Multiple alignments  5
The selection of an ad hoc score matrix is fundamental
in the case of multiple alignments
The use of an inappropriate score matrix will generate a
poor alignment
Use of a priori knowledge on the similarity degree of the
sequences to be aligned
In ClustalW, the sequences are weighed according to
their divergence from the pair of sequences most
closely related and the gap penalties and the choice of
the score matrix are based on the weight related to
each sequence
Another strategy for multiple alignment is that of not
penalizing aligned gaps
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Multiple alignments  6
Multiple alignments, as well as simple alignments, are
based solely on the similarity between nucleotide or
amino acid sequences
The similarity between sequences is an important
indicator of functional similarities, even if molecular
biologists often have additional knowledge about the
structure or the function of a particular protein or gene
Information on the secondary structure, on the presence
of superficial loops, on the localization of active sites
may be used to adjust multiple alignments “by hand”, in
order to produce biologically significant results
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Concluding…  1
An alignment of two or more genetic or polypeptide
sequences represents a hypothesis on the pathway
through which two homologous sequences have
evolved by diverging from a common ancestor
While the evolutionary path cannot be deduced with
certainty, alignment algorithms can be used to identify
“similarities” that have a low probability to occur at
random
The choice of the score function is crucial for the
quality of the resulting alignment
Use of score matrices, such as PAM and BLOSUM
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Concluding…  2
The
Needleman-Wunsch
algorithm,
for
global
alignments, and the technique by Smith and
Waterman, for local alignments, constitute the
fundamental basis on which numerous database
search algorithms were built
BLAST
FASTA
Clustal
These algorithms use indexing techniques, heuristics,
and fast comparative methods to get a quick
comparison between a query sequence and an entire
database
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